Aim: How do we find all possible values of a trig function on a unit circle?
In this lesson we will find all the values of an angle on the unit circle. Remember that an ordered pair represents cos and sin. For example the point (1,2): cos x = 1 and sin x = 2. an ordered pair can be written as (cos, sin) where the cos is the x value and sin is the y value.
Also remember that this relates to the quadrants. Answer the following:
In what quadrant is x positive? In what quadrants is x negative? These are the same for cosine.
In what quadrants is y positive? In what quadrants is y negative? These are the same for sine.
The instructor in the video stated that the reference angle stays the same in each quadrant. Sometimes a decimal value is given. When that happens, use your calculator to convert that to a measure. That is your reference angle. Sketch this in the quadrants with the proper sign. Use your reference angle to figure out the two angles that will give you the angle value.
Classwork:
1. If sin x = .7424, find, to the nearest degree, the two positive values of angle x that are less than 360 degrees.
2. If cos a = -0.3090, find, to the nearest degree, the two values of angle a to the nearest degree for 0< a <360.
In this lesson we will find all the values of an angle on the unit circle. Remember that an ordered pair represents cos and sin. For example the point (1,2): cos x = 1 and sin x = 2. an ordered pair can be written as (cos, sin) where the cos is the x value and sin is the y value.
Also remember that this relates to the quadrants. Answer the following:
In what quadrant is x positive? In what quadrants is x negative? These are the same for cosine.
In what quadrants is y positive? In what quadrants is y negative? These are the same for sine.
Video
The instructor in the video stated that the reference angle stays the same in each quadrant. Sometimes a decimal value is given. When that happens, use your calculator to convert that to a measure. That is your reference angle. Sketch this in the quadrants with the proper sign. Use your reference angle to figure out the two angles that will give you the angle value.
2. If cos a = -0.3090, find, to the nearest degree, the two values of angle a to the nearest degree for 0< a <360.
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A-8.8_Two_Trig_Values.JPG